I like maths because I enjoy solving problems. I like the feeling of challenge, the sense of intellectual stimulation, the satisfaction of getting the right answer. I particularly love that feeling you get when you're in the flow. Do you know what I mean? The feeling that time no longer matters, where distractions cease to distract, where you find yourself in an almost trance-like state, entirely concentrating on the task in hand.
Perhaps there are maths teachers out there who can induce a similar atmosphere in their classrooms. Maybe. Maybe their students get in "the flow" when faced with solving quadratic equations or using circle theorems. Maybe. Just maybe.
I'm certainly not one of those teachers. Sometimes my students are happy to get stuck in to a puzzle (re-arranging difficult formulae with y10 went down better than I expected) but too much maths without a context usually turns them off.
So I jumped at the chance when a colleague of mine suggested having a "teacher mash-up" where we would team teach my y9 maths class and give them a politics lesson with a bit of maths thrown in. He had a resource called "Prime Minister for A Day" where you are given a list of govenrment run programmes and £500 million to spend of them. As a politics taster lesson it's already got a bit of numeracy in there because the students have to add and subtract large numbers, but we felt there could be more mathematics involved if we scratched the surface.
We started by putting a more contemporaneous spin on things by giving the y9s the same list and telling them they had to cut 4.25 billion of spending. This meant cutting approximately 75% of the programmes on the list. We then gave them some pie charts represting opinion poll data from different groups of people. I created the pie charts and had a go at exaggerating the opinions of differnet groups of people such as pensioners, young mothers, guardian readers, business people, daily mail readers and 11-17 year olds.
We talked to the students about sampling and opinion poll data. They recapped what they had recently learned in their data handling project about stratified sampling and how that could give a more accurate picture of the views of the whole country. We talked about what the number 4.25 billion actually looks like (and eventually got it right after I messed it up the first time!). They discussed the huge numbers involved in government spending.
The lesson was great fun and my colleague delivered it brilliantly, but for me the best moments came when I realised how much my sutdents already knew. Eariler in the year we had done a project called "money matters" where they looked at wages, salaries, rent and bills. I'd given them articles from BBC news about average salaries and the difference between high and low earners and the students had clearly taken it on board. Near the beginning of the lesson they discussed the taxation system and whether rich people should pay more. They gave an impressively accurate figure for the average salary (£26,000). They had a discussion about what percentage of the population might be considered rich and made the point that the top 10% of earners are quite spread out. They knew that the super-rich didn't constutite 10% of the population.
At the end of the lesson they hadn't ticked off any new objectives in the national curriculum. But they had furthered their understanding of government finances, sampling techniques and large numbers. AND they had practiced debating, empathy, and rational decision making. All in all, a worthwhile lesson.
Wednesday, 20 February 2013
Wednesday, 13 February 2013
Bullseye! The mathematics of the dartboard....
Playing darts is a great way to help kids improve their numeracy skills - its fun, fast paced, and helps them improve their addition, subtraction and multiplication skills.
But the dartboard has a lot more to offer in terms of mathematics. Our department recently used it to both teach and assess a range of different skills.. and have a bit of fun in the process.
The project
At the beginning of this school year we ran a project with all of y7 and y8 about the mathematics of the dartboard. We began by getting all of them (yes EVERY SINGLE ONE - and we have got some very weak students) to construct their own dartboard using a ruler, compass and protractor. It took some of them several attempts, but in the end they produced some great work and improved their construction skills.
Then we asked them to complete a series of levelled challenges. They ranged from level 3 to level 7 and incoporated basic arithmetic skills, problem solving with numbers, reasoning about multiples, and thinking about how to approach a long task systematically.
Here are some example challenge cards
I really enjoyed doing this project with my classes and I'm looking forward to running it again next year with a few improvements. A key development for me came through the input of an English teacher in SLT who teaches some KS3 maths. She put together an assessment grid for us which enabled us to break the project down into a list of very specific skills and assess each student on every skill.
The fun stuff
The project itself was quite enjoyable to do and lots of students really enjoyed creating their own dartboards, but it really came into its own when we set up an inter-house competition linked to the project.
We invited all of y7 and y8 to take part and had about 100 students in total in the sportshall. We lined them up in their house groups infront of 7 different magnetic dartboards (one for each house). At the word GO! they began their team game of 501 down.
Here's how it worked. Each player had 3 darts. They threw their darts and worked out their total, then took away their total from the running total of their team. The next player could only take their shot when the previous player had worked out the correct answer. Maths teachers refereed each team and checked all their calculations.
It was very fast paced and the kids loved it. They were encouraging each other to use different addition and subtraction strategies "break the number down into tens and units", "take away the hundred first!" and generally having a great time doing mental arithmetic. Who would have thought it?
I've since had several y7 students ask me when the next maths related competition will be. Suggestions anyone?
But the dartboard has a lot more to offer in terms of mathematics. Our department recently used it to both teach and assess a range of different skills.. and have a bit of fun in the process.
The project
At the beginning of this school year we ran a project with all of y7 and y8 about the mathematics of the dartboard. We began by getting all of them (yes EVERY SINGLE ONE - and we have got some very weak students) to construct their own dartboard using a ruler, compass and protractor. It took some of them several attempts, but in the end they produced some great work and improved their construction skills.
Then we asked them to complete a series of levelled challenges. They ranged from level 3 to level 7 and incoporated basic arithmetic skills, problem solving with numbers, reasoning about multiples, and thinking about how to approach a long task systematically.
Here are some example challenge cards
I really enjoyed doing this project with my classes and I'm looking forward to running it again next year with a few improvements. A key development for me came through the input of an English teacher in SLT who teaches some KS3 maths. She put together an assessment grid for us which enabled us to break the project down into a list of very specific skills and assess each student on every skill.
The fun stuff
The project itself was quite enjoyable to do and lots of students really enjoyed creating their own dartboards, but it really came into its own when we set up an inter-house competition linked to the project.
We invited all of y7 and y8 to take part and had about 100 students in total in the sportshall. We lined them up in their house groups infront of 7 different magnetic dartboards (one for each house). At the word GO! they began their team game of 501 down.
Here's how it worked. Each player had 3 darts. They threw their darts and worked out their total, then took away their total from the running total of their team. The next player could only take their shot when the previous player had worked out the correct answer. Maths teachers refereed each team and checked all their calculations.
It was very fast paced and the kids loved it. They were encouraging each other to use different addition and subtraction strategies "break the number down into tens and units", "take away the hundred first!" and generally having a great time doing mental arithmetic. Who would have thought it?
I've since had several y7 students ask me when the next maths related competition will be. Suggestions anyone?
Friday, 8 February 2013
Real Life Maths: Circle Theorems and Ship Navigation
Eureka! I have just found a truly shiny thing. A prized possession in my magpie collection of shiny resources.
A video that explains why CIRCLE THEOREMS are useful.
Hooray! I love circle theorems. I love the way you have to visualise shapes inside a complex diagram, but once you've seen the visual links, the actual calculations are not hard at all. They make for lots of lovely "ohhhh, I get it" moments.
The only problem I have with teaching circle theorems is that I can never think of a practical use for them. But I've just found one: Calculating the distance of the visible horizon.
Here is the link: http://www.youtube.com/watch?v=VRvvtOAHDG0&feature=player_embedded
Its particularly good because the nice young man in the video explains why maths is so important to his job first, then gives you a lovely clear example of how to use the circle theorem that the angle between the tangent and a radius is 90 degrees.
The only problem is that I just taught that topic to y11 today. I wish I'd found it yesterday!
.
A video that explains why CIRCLE THEOREMS are useful.
Hooray! I love circle theorems. I love the way you have to visualise shapes inside a complex diagram, but once you've seen the visual links, the actual calculations are not hard at all. They make for lots of lovely "ohhhh, I get it" moments.
The only problem I have with teaching circle theorems is that I can never think of a practical use for them. But I've just found one: Calculating the distance of the visible horizon.
Here is the link: http://www.youtube.com/watch?v=VRvvtOAHDG0&feature=player_embedded
Its particularly good because the nice young man in the video explains why maths is so important to his job first, then gives you a lovely clear example of how to use the circle theorem that the angle between the tangent and a radius is 90 degrees.
The only problem is that I just taught that topic to y11 today. I wish I'd found it yesterday!
.
Tuesday, 5 February 2013
Get off the escalator! An Experiment in Independent Learning
Yet again this is something that I was inspired to do by the Jim Smith (aka the lazy teacher). In our INSET session back in January he showed us this video: http://www.youtube.com/watch?v=VrSUe_m19FY
In the video, two well-dressed people are shown standing on a moving escalator. The escalator suddenly stops working and the people start to panic. "I'm already late" moans the woman. "Someone will come to help" says the man. They stand there looking increasingly foolish, but it doesn't occur to either of them to simply WALK up the escalator.
I showed this video to my year 9s and they thought it was hilarious. Then I asked them - does anyone ever act like this at school? And they came up with loads of examples: students who say they couldn't start their work because they didn't get a worksheet when there was actually a pile of spares at the front, students who get stuck on a question and sit there waiting for help when they could just move on to the next one and come back to it later, etc. etc. They are all trivial examples of Dweck's "learned helplessness" idea.*
Then I showed them clips from these two videos about the "hole in the wall" project.
http://www.ted.com/talks/sugata_mitra_shows_how_kids_teach_themselves.html
and
http://www.ted.com/talks/sugata_mitra_the_child_driven_education.html
The gist of these videos is that some children in India were given access to computers and by using the computers they were able to teach themselves high level skills in various different subjects.
My year 9 class were suitably impressed. Personally I think the results of the hole in the wall experiment are much more nuanced than these videos allow, but the message that children can research and learn things for themselves is certainly important.
So I challenged my year 9 class to do a similar thing. I put them into groups of 6 and gave them 6 data handling topics, along with outcomes, objectives and sample questions. The topics were: Random and Stratified Sampling, Pie Charts, Box Plots, Scatter Graphs and Cumulative Frequency. I asked them to research the topics themselves and prepare mini lessons to teach the others in their group. At the end of the cycle of lessons I gave them the data from the old GCSE coursework project "Mayfield High" and asked them to use all the techniques they had just learned to investigate different hypotheses.
The projects are due in this Thursday, so I haven't started marking them yet, but I'm pretty optimistic about them so far. Apart from a couple of notable exceptions, the year 9s really took on the challenge of researching and delivering their own lessons and I think they did a great job. One of them even got her students to do a test at the end of her lesson to check their progress!
I don't intend to let my y9s teach themselves everything but it has certainly inspired me to take more risks with student led learning. AND I now have a great phrase to use when one of them starts falling into the trap of "learned helplessness. I just say "Get off the escalator!" and they know they should figure it out for themselves.
:)
*(Just as a little aside - a lot of teachers will be nodding their heads now thinking of students who act like this, but adults do it too! A friend told me this story recently about her parents: her dad was in the shower when he suddenly started to shout downstairs to his wife. "Sarah! Sarah!" he cried in desparation. "What is it?" she said, in a slightly worried tone. What could have happened to cause so much concern? The reply - "I've put the conditioner on first!! What do I do?)
In the video, two well-dressed people are shown standing on a moving escalator. The escalator suddenly stops working and the people start to panic. "I'm already late" moans the woman. "Someone will come to help" says the man. They stand there looking increasingly foolish, but it doesn't occur to either of them to simply WALK up the escalator.
I showed this video to my year 9s and they thought it was hilarious. Then I asked them - does anyone ever act like this at school? And they came up with loads of examples: students who say they couldn't start their work because they didn't get a worksheet when there was actually a pile of spares at the front, students who get stuck on a question and sit there waiting for help when they could just move on to the next one and come back to it later, etc. etc. They are all trivial examples of Dweck's "learned helplessness" idea.*
Then I showed them clips from these two videos about the "hole in the wall" project.
http://www.ted.com/talks/sugata_mitra_shows_how_kids_teach_themselves.html
and
http://www.ted.com/talks/sugata_mitra_the_child_driven_education.html
The gist of these videos is that some children in India were given access to computers and by using the computers they were able to teach themselves high level skills in various different subjects.
My year 9 class were suitably impressed. Personally I think the results of the hole in the wall experiment are much more nuanced than these videos allow, but the message that children can research and learn things for themselves is certainly important.
So I challenged my year 9 class to do a similar thing. I put them into groups of 6 and gave them 6 data handling topics, along with outcomes, objectives and sample questions. The topics were: Random and Stratified Sampling, Pie Charts, Box Plots, Scatter Graphs and Cumulative Frequency. I asked them to research the topics themselves and prepare mini lessons to teach the others in their group. At the end of the cycle of lessons I gave them the data from the old GCSE coursework project "Mayfield High" and asked them to use all the techniques they had just learned to investigate different hypotheses.
The projects are due in this Thursday, so I haven't started marking them yet, but I'm pretty optimistic about them so far. Apart from a couple of notable exceptions, the year 9s really took on the challenge of researching and delivering their own lessons and I think they did a great job. One of them even got her students to do a test at the end of her lesson to check their progress!
I don't intend to let my y9s teach themselves everything but it has certainly inspired me to take more risks with student led learning. AND I now have a great phrase to use when one of them starts falling into the trap of "learned helplessness. I just say "Get off the escalator!" and they know they should figure it out for themselves.
:)
*(Just as a little aside - a lot of teachers will be nodding their heads now thinking of students who act like this, but adults do it too! A friend told me this story recently about her parents: her dad was in the shower when he suddenly started to shout downstairs to his wife. "Sarah! Sarah!" he cried in desparation. "What is it?" she said, in a slightly worried tone. What could have happened to cause so much concern? The reply - "I've put the conditioner on first!! What do I do?)
Saturday, 2 February 2013
Cross Curricular maths: Codes and Codebreakers
About a year ago I gave a talk to a group of maths students at a careers event at Oxford University. I endeavoured to persuade them to ignore all offers of ridiculously highly paid jobs in the city and become secondary maths teachers instead. Not an easy task. So I was pleasantly suprised when quite a few students came up to speak to me at the end of all the talks.
I was particularly surprised that anyone bothered to speak to me because the speaker who came directly before me was from GCHQ. He worked as a codebreaker and was incredibly cool.
Mathematicians are in high demand at GCHQ he said. The work is really interesting and it pays well. Where else could you say that your mathematical skills were being put to use to help protect the nation? You'll be serving Queen and Country from a very comfortable office in Cheltenham.
Powerful stuff.
Even more enticing - he pointed out that codebreakers weren't allowed to take work home and were strongly discouraged from staying later than 5pm. I started to have doubts about my chosen career.....
To remind myself that teaching really is the best job in the world, I decided that I could have a go at being a codebreaker myself and I'd get my year 8 class to join in. I used some resources from Nrich, out of which I particularly like the transposition cipher because it helps cement understanding of factors and multiples http://nrich.maths.org/7940.
This year we're going one step further and one of my wonderful colleagues in the history department has got involved. We're rolling out the codebreaking project to the whole of year 8 and putting it in the context of WW2 codebreakers at Bletchly park. (This context has the major advantage of demonstrating how women can be excllent mathematicians too. Girls need mathematical role models). This is the first slide:
The history teacher gave me some sentences in English which I have coded using different techniques including the ceasar shift technique, the pigpen cipher, a transposition cipher and the vigenere square. I used Simon Singh's wonderful website to help me out. It does the ciphering for you! http://www.simonsingh.net/The_Black_Chamber/chamberguide.html And it gives some really useful historical context to each technique.
I was particularly surprised that anyone bothered to speak to me because the speaker who came directly before me was from GCHQ. He worked as a codebreaker and was incredibly cool.
Mathematicians are in high demand at GCHQ he said. The work is really interesting and it pays well. Where else could you say that your mathematical skills were being put to use to help protect the nation? You'll be serving Queen and Country from a very comfortable office in Cheltenham.
Powerful stuff.
Even more enticing - he pointed out that codebreakers weren't allowed to take work home and were strongly discouraged from staying later than 5pm. I started to have doubts about my chosen career.....
To remind myself that teaching really is the best job in the world, I decided that I could have a go at being a codebreaker myself and I'd get my year 8 class to join in. I used some resources from Nrich, out of which I particularly like the transposition cipher because it helps cement understanding of factors and multiples http://nrich.maths.org/7940.
This year we're going one step further and one of my wonderful colleagues in the history department has got involved. We're rolling out the codebreaking project to the whole of year 8 and putting it in the context of WW2 codebreakers at Bletchly park. (This context has the major advantage of demonstrating how women can be excllent mathematicians too. Girls need mathematical role models). This is the first slide:
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